This project investigates the synthesis of effective algebraic and numerical algorithms and on their practical and theoretical improvement. This includes the comprehensive study of practical numerical algorithms for polynomial rootfinding, which is a central subject of algebraic computing. The study should include many technical novelties. Another fundamental subject covered by the project and having ubiquitous applications to many areas of scientific and engineering computing and signal processing is the computations with structured matrices. The project also includes various extensions and applications of polynomial rootfinding and structured matrices, in particular to approximating polynomial gcd, to polynomial interpolation and multipoint evaluation, and to solving polynomial systems of equations. The work also applies to sign determination and modular reduction, which is a central subject of algebraic and geometric computations, and on decoding the BCH error-correcting codes, in particular Reed-Solomon codes most important in practice.
